Department of

# Mathematics

Seminar Calendar
for events the day of Monday, October 20, 2014.

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events for the
events containing

Questions regarding events or the calendar should be directed to Tori Corkery.
    September 2014          October 2014          November 2014
Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa
1  2  3  4  5  6             1  2  3  4                      1
7  8  9 10 11 12 13    5  6  7  8  9 10 11    2  3  4  5  6  7  8
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30


Monday, October 20, 2014

3:00 pm in 341 Altgeld Hall,Monday, October 20, 2014

#### Inertia spaces and the cyclic homology of convolution algebras over proper Lie groupoids

###### Markus Pflaum (University of Colorado)

Abstract: The inertia space of a Lie groupoid encodes interesting topological, geometric, and analytic information about the original Lie groupoid. It is the goal of the talk to explain this point of view using as example the cyclic homology theory of the convolution algebra of a proper Lie groupoid. To this end, the inertia groupoid associated to a proper Lie groupoid is first defined. We show that it is a differentiable stratified groupoid, and non-singular only in exceptional cases. The corresponding quotient space, the inertia space, possesses a Whitney stratification, and is triangulable. Finally, horizontal and basic forms over the inertia space are constructed, and a Hochschild-Kostant-Rosenberg type theorem for the convolution algebra of a proper Lie groupoid is indicated. The talk is based upon joint work, partially in progress, with H. Posthuma and X. Tang, as well as with C. Farsi and Ch. Seaton.

4:00 pm in 243 Altgeld Hall,Monday, October 20, 2014

#### Commutative rings in equivariant stable homotopy theory

###### Mychael Sanchez (UIUC Math)

Abstract: In non-equivariant homotopy theory, E infinity rings play a fundamental role. In the equivariant setting, there are two distinct, but useful notions of an “E infinity" ring spectrum. I’ll discuss both approaches, give examples, and compare them by means of a forgetful functor. This forgetful functor has a left adjoint and a “homotopical” right adjoint. To make sense of this, one needs a suitable equivariant stable category. I’ll motivate such a category by discussing the role that representation spheres play in the equivariant generalizations of classical theorems in stable homotopy theory.

5:15 pm in Altgeld Hall,Monday, October 20, 2014

#### weakly right injective operator systems

###### Ali Kavruk (UIUC)

Abstract: We study WEP for operator systems.